where we had defined <math>e</math> as being the maximum height of the drop:

<math>e=2\kappa^{-1}\sin{\frac{\theta_e}{2}}</math>

and <math>\kappa=\sqrt{\frac{\rho g}{\sigma_{lv}}}</math> was the inverse capillary length.

To visualize what the edge of a large drop then looks like, you can use the following two MATLAB programs (see below), which will solve and plot the above differential equation. Figure 1 also shows what some of these plots look like.

In class we had a brief discussion as to the nature of the drop's periphery on superhydrophobic surfaces. In the superhydrophobic limit (i.e., as <math>\theta_e</math> approaches 180 degrees), will the edge of the drop have a semicircular shape? The shape is apparently not semicircular at 179 degrees, since the horizontal range of the drop is only 1 mm, while it vertically extends to a height of

<math>2\kappa^{-1}\approx 3.5 \text{mm}</math>

Nevertheless, the bottom left corner of the 179 degree profile does resemble a quarter-circle.

MATLAB code

To visualize your own large drop profiles, copy and paste the following two MATLAB scripts into two corresponding files. Then run dropshape.m -- it will automatically plot the profile. You can adjust the contact angle by variying the parameter "angle" in dropshape.m.